UKMT Grey Kangaroo, 2021

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

Three villages are connected by paths as shown. From Downend to Uphill, the detour via Middleton is 1 km longer than the direct path. From Downend to Middleton, the detour via Uphill is 5 km longer than the direct path. From Uphill to Middleton, the detour via Downend is 7 km longer than the direct path. What is the length of the shortest of the three direct paths between the villages?

(A) $1\text{ km}$ (B) $2\text{ km}$ (C) $3\text{ km}$ (D) $4\text{ km}$ (E) $5\text{ km}$

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